The top U.S. diplomat took a step toward that goal on Sunday, meeting with Russian Foreign Minister Sergei Lavrov on the sidelines of a major summit in Manila, Philippines.
The face-to-face meeting is the first since President Trump last week begrudgingly signed into law legislation that not only sanctions Russia, Iran, and North Korea, but also ties the president's hands from making changes to the penalties without congressional approval.
The meeting between the two envoys Sunday also followed Moscow's retaliating over the new sanctions by seizing two American diplomatic properties and ordering a huge cut in the U.S. diplomatic staff by over 700.
It's unclear how many of those in the U.S. diplomatic staff in Russia are Americans. The majority are Russian locals employed by the American government.
But Lavrov explained to Tillerson how Russia plans to follow through on its demand for a U.S. personnel cut, Lavrov told Russian media after the meeting.
"He was interested most of all" in this, Lavrov added, blaming "the Russophobia inclination of the members of Congress" for sparking Russia's retaliation. Trump tweeted something similar last week, saying "You can thank Congress" for the "all-time and very dangerous low."
Lavrov also said the Trump administration is ready to push forward toward cooperation -- something Tillerson has also said he wants.
"We felt the readiness of our U.S. colleagues to continue dialogue. I think there's no alternative to that," Lavrov said Sunday, according to Reuters.
That echoed what Tillerson told reporters Tuesday, "We can’t let [sanctions] take us off track of trying to restore the relationship."
During a photo-op before their meeting, Tillerson and Lavrov shared smiles and some pleasantries, but both ignored a question on how the new sanctions will impact their talks.
The American side has not provided a readout of the meeting, but Tillerson's senior aide R.C. Hammond said in an email to ABC News that "Day 1" at the summit in Manila was "productive... Still a lot to do."
The Trump administration has been seeking closer ties to Russia, especially on fighting ISIS and pressuring North Korea. But between Trump's praise for Russian President Vladimir Putin and his skepticism of the U.S. intelligence community's finding that Russia interfered in the U.S. election, the Republican-controlled Congress took extraordinary measures to curtail the power of a president from their own party.
Tillerson has made clear that he and Trump did not support the legislation, but would enforce it now that it's law.
Still, the Kremlin and the White House will try to move past the hurdles to work together on Syria and Ukraine. Lavrov announced that Tillerson's special envoy for Ukraine negotiations, former ambassador to NATO Kurt Volker, will travel to Russia soon to discuss the conflict. And the two countries continue to discuss expanding their limited cease-fire with Jordan in Syria's southwest corner, weeks after it was implemented and which has seen few violations.
ABC News's Patrick Reevell contributed to this report.